Question

An electric power station transmits $100 \,MW$ power through long and thin cable. If the transmission is at
(i) $20000 \,V$,
(ii) $200\, V$,
in which case would be less power loss?

• A. In (i) only
• B. In (ii) only
• C. In each case, power loss is zero
• D. Data is insufficient

Answer 1

Answer: (A)

Power dissipated is given by $P=V I$
where $V$ is voltage and $I$ is current.
First case, $I_{1}=\frac{P}{V_{1}}=\frac{100 \times 10^{6}}{20000}=5000\, A$
Second case, $I_{2}=\frac{P}{V_{2}}=\frac{100 \times 10^{6}}{200}=500000 \,A$
Also, power dissipated is given by $P=I^{2} R$
where $R$ is resistance of the cable.
$\therefore P_{1}=(5000)^{2} R=25 \times 10^{6} R$
$P_{2}=(500000)^{2} R=25 \times 10^{10} R$
$\Rightarrow P_{1} < P_{2}$